Fluid Mechanics Assignment 6 — Viscous Fluid Flow  
$$ \sum F_y= m \frac{{\rm d} v}{{\rm d} t}$$ and from the shear stresses: $$ \tau_{xy}=\mu\frac{\partial v}{\partial x}~~~~\tau_{yy}=\mu\frac{\partial v}{\partial y}~~~~\tau_{zy}=\mu\frac{\partial v}{\partial z}$$ Prove the $y$component of the momentum equations for a viscous fluid: $$ \rho \left(\frac{\partial v}{\partial t} + u \frac{\partial v}{\partial x} + v \frac{\partial v}{\partial y} + w \frac{\partial v}{\partial z} \right) = \frac{\partial P}{\partial y} + \mu \frac{\partial^2 v}{\partial x^2} + \mu \frac{\partial^2 v}{\partial y^2} + \mu \frac{\partial^2 v}{\partial z^2} +B_y $$ Outline all assumptions. 














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